How to simplify the function and get the omega out of the sqrt[]? I give some assumptions and hope that Mathematica can simplify the expression to the result as shown in the figure. Is there any method to solve this problem? Image

  • $\begingroup$ Assuming[{w > 0}, w Simplify[ Sqrt[w^2 + w^4/w0^2] / w] ] gives something close. $\endgroup$
    – LouisB
    Nov 5, 2016 at 10:20
  • 2
    $\begingroup$ Please, post code not pics! $\endgroup$
    – user9660
    Nov 5, 2016 at 10:25

1 Answer 1


Not the form that you specified, but it does pull an ω out of the Sqrt

expr = Sqrt[ω^2 + ω^4/Subscript[ω, 0]^2]

enter image description here

Define a ComplexityFunction

cf = (Total[Cases[#, Power[_, n_] :> n, Infinity]^2] + LeafCount[#]) &;

Simplify[expr, {ω > 0, Subscript[ω, 0] > 0},
 ComplexityFunction -> cf]

enter image description here


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